Computes a weighted sum of squares matrix

はじめる前に
新機能一覧
Maple ワークシートの作成
Mapleワークシートを共有
Maple ウィンドウのカスタマイズ
Maple システムのカスタマイズ
コネクティビティ
Mathematics
数学
物理
プログラミング
グラフィックス
Student パッケージ
Science and Engineering
科学・エンジニアリング
アプリケーションと例題
リファレンス
システム
MapleSim
MapleSim ツールボックス
MapleSim ヘルプ
Tasks
Toolboxes
- BlockImporter
- Global Optimization
- Grid Computing
- Maple-NAG Connector
  - General information
  - Computational Routines
    - a02 (Complex Arithmetic)
    - c02 (Zeros of Polynomials)
    - c05 (Roots of One or More Transcendental Equations)
    - c06 (Fourier Transforms)
    - d01 (Quadrature)
    - d02 (Ordinary Differential Equations)
    - d03 (Partial Differential Equations)
    - d06 (Mesh Generation)
    - e01 (Interpolation)
    - e02 (Curve and Surface Fitting)
    - e04 (Minimizing or Maximizing a Function)
    - f01 (Matrix Factorizations)
    - f02 (Eigenvalues and Eigenvectors)
    - f03 (Determinants)
    - f04 (Simultaneous Linear Equations)
    - f06 (Linear Algebra Support Functions)
    - f07 (Linear Equations (LAPACK))
    - f08 (Least-squares and Eigenvalue Problems (LAPACK))
    - f11 (Large Scale Linear Systems)
    - f16 (NAG Interface to BLAS)
    - g01 (Simple Calculations on Statistical Data)
    - g02 (Correlation and Regression Analysis)
      - g02 Introduction
      - g02brc (nag_ken_spe_corr_coeff)
      - g02btc (nag_sum_sqs_update)
      - g02buc (nag_sum_sqs)
      - g02bwc (nag_cov_to_corr)
      - g02bxc (nag_corr_cov)
      - g02byc (nag_partial_corr)
      - g02cac (nag_simple_linear_regression)
      - g02cbc (nag_regress_confid_interval)
      - g02dac (nag_regsn_mult_linear)
      - g02dcc (nag_regsn_mult_linear_addrem_obs)
      - g02ddc (nag_regsn_mult_linear_upd_model)
      - g02dec (nag_regsn_mult_linear_add_var)
      - g02dfc (nag_regsn_mult_linear_delete_var)
      - g02dgc (nag_regsn_mult_linear_newyvar)
      - g02dkc (nag_regsn_mult_linear_tran_model)
      - g02dnc (nag_regsn_mult_linear_est_func)
      - g02eac (nag_all_regsn)
      - g02ecc (nag_cp_stat)
      - g02eec (nag_step_regsn)
      - g02fac (nag_regsn_std_resid_influence)
      - g02fcc (nag_durbin_watson_stat)
      - g02gac (nag_glm_normal)
      - g02gbc (nag_glm_binomial)
      - g02gcc (nag_glm_poisson)
      - g02gdc (nag_glm_gamma)
      - g02gkc (nag_glm_tran_model)
      - g02gnc (nag_glm_est_func)
      - g02hac (nag_robust_m_regsn_estim)
      - g02hbc (nag_robust_m_regsn_wts)
      - g02hdc (nag_robust_m_regsn_user_fn)
      - g02hfc (nag_robust_m_regsn_param_var)
      - g02hkc (nag_robust_corr_estim)
      - g02hlc (nag_robust_m_corr_user_fn)
      - g02hmc (nag_robust_m_corr_user_fn_no_derr)
    - g03 (Multivariate Methods)
    - g04 (Analysis of Variance)
    - g05 (Random Number Generators)
    - g07 (Univariate Estimation)
    - g08 (Nonparametric Statistics)
    - g10 (Smoothing in Statistics)
    - g11 (Contingency Table Analysis)
    - g12 (Survival Analysis)
    - g13 (Time Series Analysis)
    - h (Operations Research)
    - m01 (Sorting)
    - s (Approximations of Special Functions)
    - x01 (Mathematical Constants)
    - x02 (Machine Constants)
    - x04 (Input-Output Utilities)
  - Getting Started
  - Example Worksheet
エラーメッセージガイド
マニュアル
数学アプリ

NAG[g02buc] NAG[nag_sum_sqs] - Computes a weighted sum of squares matrix

Calling Sequence

g02buc(mean, n, x, sw, wmean, c, 'm'=m, 'wt'=wt, 'fail'=fail)

nag_sum_sqs(. . .)

Parameters

mean - String;

On entry: indicates whether nag_sum_sqs (g02buc) is to calculate sums of squares and cross-products, or sums of squares and cross-products of deviations about the mean.

The sums of squares and cross-products of deviations about the mean are calculated.

The sums of squares and cross-products are calculated.

Constraint: "Nag_AboutMean" or "Nag_AboutZero". .

n - integer;

On entry: , the number of observations in the data set.

Constraint: . .

x - Matrix(1..dim1, 1..m, datatype=float[8], order=order);

Note: this array may be supplied in Fortran_order or C_order , as specified by order. All array parameters must use a consistent order.

On entry: must contain the th observation on the th variable, for and .

sw - assignable;

Note: On exit the variable sw will have a value of type float.

On exit: the sum of weights.

If , sw contains the number of observations, .

wmean - Vector(1..m, datatype=float[8]);

On exit: the sample means. contains the mean for the th variable.

c - Vector(1.., datatype=float[8]);

Note: the dimension, dim, of the array c must be at least .

On exit: the cross-products.

If , c contains the upper triangular part of the matrix of (weighted) sums of squares and cross-products of deviations about the mean.

If , c contains the upper triangular part of the matrix of (weighted) sums of squares and cross-products.

These are stored packed by columns, i.e., the cross-product between the th and th variable, , is stored in .

'm'=m - integer; (optional)

On entry: , the number of variables.

Constraint: . .

'wt'=wt - Vector(1..dim, datatype=float[8]); (optional)

Note: the dimension, dim, of the array wt must be at least .

On entry: the optional weights of each observation. If weights are not provided then wt must be set to the null pointer, i.e., (double *)0, otherwise must contain the weight for the th observation.

Constraint: if , for . .

'fail'=fail - table; (optional)

The NAG error argument, see the documentation for NagError.

Description

	Purpose
	nag_sum_sqs (g02buc) calculates the sample means and sums of squares and cross-products, or sums of squares and cross-products of deviations from the mean, in a single pass for a set of data. The data may be weighted.

Description

nag_sum_sqs (g02buc) is an adaptation of West's WV2 algorithm; see West (1979). This function calculates the (optionally weighted) sample means and (optionally weighted) sums of squares and cross-products or sums of squares and cross-products of deviations from the (weighted) mean for a sample of observations on variables , for . The algorithm makes a single pass through the data.

For the first observations let the mean of the th variable be , the cross-product about the mean for the th and th variables be and the sum of weights be . These are updated by the th observation, , for , with weight as follows:

[[W[i]=W[i-1]+w[i]],[(x)[j](i)=(x)[j](i,-,1)+(w[i])/(W[i])(x[j],-,(x)[j],(i,-,1)) j=1,2,..,m]]

and

c[jk](i)=c[jk](i,-,1)+(w[i])/(W[i])(x[j],-,(x)[j],(i,-,1))(x[k],-,(x)[k],(i,-,1))W[i-1] j=1,2,..,m k=j,j+1,..,m

The algorithm is initialized by taking , the first observation, and .

For the unweighted case and for all .

Note that only the upper triangle of the matrix is calculated and returned packed by column.

	Error Indicators and Warnings
	"NE_ALLOC_FAIL" Dynamic memory allocation failed. "NE_BAD_PARAM" On entry, argument had an illegal value. "NE_INT" On entry, . Constraint: . On entry, . Constraint: . "NE_INTERNAL_ERROR" An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please consult NAG for assistance. "NE_REAL_ARRAY_ELEM_CONS" On entry, .

	Accuracy
	For a detailed discussion of the accuracy of this algorithm see Chan et al. (1982) or West (1979).

	Further Comments
	g02bwc (nag_cov_to_corr) may be used to calculate the correlation coefficients from the cross-products of deviations about the mean. The cross-products of deviations about the mean may be scaled to give a variance-covariance matrix. The means and cross-products produced by nag_sum_sqs (g02buc) may be updated by adding or removing observations using g02btc (nag_sum_sqs_update).

Examples

mean := "Nag_AboutMean":
n := 3:
m := 3:
x := Matrix([[9.123100000000001, 3.7011, 4.523], [0.931, 0.09, 0.887], [0.0009, 0.009900000000000001, 0.0999]], datatype=float[8]):
wt := Vector([0.13, 1.307, 0.37], datatype=float[8]):
wmean := Vector(3, datatype=float[8]):
c := Vector(6, datatype=float[8]):
NAG:-g02buc(mean, n, x, sw, wmean, c, 'm' = m, 'wt' = wt):

sw;

wmean;

	See Also
	Chan T F, Golub G H and Leveque R J (1982) Updating Formulae and a Pairwise Algorithm for Computing Sample Variances Compstat, Physica-Verlag West D H D (1979) Updating mean and variance estimates: An improved method Comm. ACM 22 532–555 g02 Chapter Introduction. NAG Toolbox Overview. NAG Web Site.